Zone-melting with joule heat



April 12, 1960 v w. G. PFANN 2,932,562

zoNE-MELTING WITH JOULE HEAT Filed Dec. 27, 1956 i il \\\\\\\\\\w F /G 5 mi 65 i uw a 'Nk Mmmm ,i \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\m 67 ummm 60 65 E* 66 62 uy/@2m 64 62 m F/G.5b By I u 6l 'M 2M A 7' TORNE V United States Patent O 2,932,562 ZONE-MELTING WITH JOULE HEAT William G. Pfann, Far Hills, NJ., assignor to Bell Telephone Laboratories, Incorporated, New York, NX., a corporation of New York Application December 21, 1956, senat No. 630,804 411 claims. (ci. '1s- 10) This invention relates to zone-melting methods in which molten zones are produced by loule heat and are caused to progress without the use of moving heating means. The methods herein may beused in conjunction with any zone-melting apparatus and are particularly useful in thezone-retning of reactive metals when used in conjunction with any of the crucibleless zone-melting procedures known to the art.

Developed primarily as a method of refining and controlling impurity content in semiconductive materials, the basic zone-melting processes announced to the public in 1951 have found increasingly broad application in both industry and research. 1n addition to being used in the processing of a major portion of semiconductive materials such as germanium and silicon destined for use in semiconductor' transducing devices such as rectiers and transistors, the zone-melting principle now nds application 'to such diverse objectives as the purification of orgarlic materials such as naphthalene and benzoic acid, metals such as tin, antimon'y, aluminum and iron, chemicals such as gallium trichloride, semiconductive materials of diamond-cubic and related crystal structures such as compounds of the group lIIgroup V classes of the periodic table according to Mendelyeev and to some materials which are normally molten at or near room temperature, such as water and gallium.

Various crucibleless zone-melting techniques have been developed for use in the processing of certain reactive materials such as titanium, zirconium, iron and other materials of such purity level that crucible contamination at the elevated temperature necessary to produce a Vmolten zone becomes a deterrent to the production or materials of desired impurity content. In certain or these processes 'a molten zone is produced through the entire cross-section of the ingot and is suspended between the two solid-liquid interfaces of the adjoining portions of the solid ingot, the remaining surface of the zone contacting only a protective atmosphere or being protected by an evacuated region. Such procedures include the floating zone technique of copending United States application, Serial No. 326,561, iiled December 17, 1952, in which a moving molten zone is suspendedv between two interfaces chiefly by virtue of adhesive forces between 'the molten zone and the solid portions of the ingot and cohesive forces Within the molten zone itself. Another such process is the suspension zone-melting technique of copending United States patent application Serial No. 516,221, tiled June 17, 1955, in which a molten zone is held in position between two solid-liquid interfaces in a horizontal ingot by virtue of the reactive force `resulting from the interaction of a magnetic held and a Other zone-melting Vtechniques designed to avoid Crucible contamination make use of moving molten zones' which do not penetrate the entire cross-section of the ingot being processed, the molten portion being retained primarily by adhesive forces. Such methods also include processes in which molten zone'sare passed along the top surface of the ingot such as described in United States Patent 2,739,088, issued March 20, 1956, the technique sometimes referred to as cage-zone-melting in which a molten zone extending through all but a plurality of fin-like projections of a vertical ingot is passed through the ingot and retained in position, partly by reason of adhesion of the molten material to the fin-like extremities described in Review of Scientific Instruments 26, 303 (1955), and a process in which a sector-shaped zone extending from the upper surface at least half-way through an ingot is caused to traverse the entire ingot in a spiral path by rotating the ingot during the progression of the zone.

In all of these crucibleless methods as heretofore used the difiiculty of producing steep thermal gradients within materials under treatment limits the dimension of the molten region at right angles to the direction of traversal. For example, in the tloating zone technique referred to above, especially where the material under treatment has the high thermal conductivity evidenced, for example, by most metallic materials, the use of external heating means results in a limitation on the diameter vof an ingot which may be so processed. In these techniques, where the chief limitation in producing a stable zone is the length of the zone, rather than the cross-section, the limitation in molten cross-section resulting from the use of external heaters severely limits the quantity of product so produced. l

By use of the internal heating means herein described the cross-sectional area of molten zones is made substantially independent of the thermal conductivity of the material under treatment. As applied `to the floating-zone technique this results in the practicability of passing stable zones having volumes many times as great as those producedby exterior heating means such as the ring-type heaters now commonly used. Use of this process therefore, results in increased output for a similar investment in apparatus. ln addition to this obvious application to Crucible-free zone-melting which may for the first time make treatment of certain materials by this process commercially feasible, the elimination of external heaters and the accompanying simplification of apparatus makes the use of the processes herein described advantageous in the conventional zone-melting of many materials.

rucible zone-melting processes to which the techniques of this invention are applicable include those using barshaped solid-ingots as well as those using powder, composite bar and helical and other non-bar-shaped starting bodies. s

In accordance with this invention a molten zone is created in an ingot of a non-insulating material by passingeither an alternating or direct current through the ingot, the current being of such magnitude that the 12R heat (Joule heat) is suicient to raise the ingot to its melting point. The length of the molten zone so formed is restricted by use of heat sinks which may, for example, take the form of air-cooled or water-cooled clamps at the extremities of the ingot. Use of such heat sinks resuits in a double temperature gradient with the` low ends at the extremities of the ingot and a high temperature region intermediate the extremities, the latter corresponding with the position of the molten zone. If, for example,

. the heat sinks aremaintained at the same temperature the molten zone will be at a point mid-way between the cooled portions of the ingot. The zone so formed is caused to progress by varying the relative temperatures of the two heat sinks, zone travel being produced in a direction away from the cooler of the sinks. If it is desired to maintain the length of the molten zone constant during progression, the vtemperatures of the two sinks are programmed simultaneously, one being cooled and the temperature of the other being raised. Further control of molten zone position and length and improvement in heat efliciency may be elfected by use of reflectors and sinks as Iwill be described. Methods for compensating for thermal expansion and contraction during the process will also be discussed.

A chief advantage of the processes of this invention results from the generation of the heat vrequired to produce and maintain the zone within the ingot itself, thereby avoiding the difficulties associated with the use of external heaters. As will be discussed in detail, in certain systems, such for example as the usual metallic system, a decrease in the value of electrical conductivity and/or thermal conductivity in the molten phase as compared advantage in that a larger amount of heat is generated in the precise position in which it is desired, that is, within the molten zone. As will also be discussed the invention is, however, not to be limited to operation on such systems in which electrical and/or thermal conductivity decreases in the molten zone, but is effective for use in a broader range of systems, the limiting character# istics of which are set forth herein.

For convenience in describing the invention reference willbe had to the following figures in which:

Fig. 1 is a schematic front elevation view of an ingot being zone-melted and zone-melting apparatus in accordance with the present invention;

. Fig. 2 depicts graphically the temperature gradients in an ingot such as that of Fig. l during processing;

Fig. 3 is a schematic front elevation in section of an ingot undergoing zone-melting in accordance with the lprocesses herein in which a moving reflector is used to effect further'cont-rol over the movement and dimensions of the molten zone; f Pig. 4 is a schematic front elevation in section of an ingotundergoing the treatment of'Fig. 3 but in which process moving heat absorbers are used in addition to the moving heat rellector;

Fig. 5a is a schematic front elevation in section of an ingot undergoing zone-melting treatment on an apparatus designed to compensate for thermal expansion and contraction resulting during treatment; and

Fig. 5b is an end view of the ingot and apparatus of Fig. 5a.

Referring again to Fig. l ingot 1, which in this instance is rod-shaped, and which may, for example, be iron or other material meeting the requirements set forth below, is held in clamps 2 and 3. Means are provided for varying the temperatures of clamps 2 and 3 over a range below the melting point of the material of ingot 1. In the apparatus depicted clampsI 2 and 3 are hollow kand arel water-cooled, water passing in inlet 4 and out outlet 5 in clamp 2 and in inlet 6 and out outlet 7 in clamp 3. The required temperature variation may result either from a variation in the flow rate of water or other coolant through clamps 2 and 3, by a variation in the temperature of the coolant or by a combination of the two. An electrical current produced by battery or other electrical power source 8 is caused to flow successively through wire 9,- electrode contact 10, clamp 2, ingot 1, clamp 3, electrode contact 11 and wire 12. The current thereby produced is such that the resultant Joule heat is sucient to melt ingot 1. Molten zone 13, thereby produced, is prevented from expanding beyond solid-liquid interfaces l14 and 15 by virtue of the axial heat loss directed from inter- .face 14 to cooling clamp 2 and from interface 15 to cooling clamp 3. The depicted olf-center position of molten zone 13 in respect to clamps 2 and 3 indicates that at this stage of the process clamp 3 is at a lower temperature than clamp 2. If molten zone travel is desired from left to right, the temperatures of clamps 2 and 3 are monitored by simultaneously decreasing the temperature of clamp 2 and increasing the temperature of clamp 3. A method of setting up a program by use of which moving molten zone 13 is maintained at a fixed length during traversal will be set forth. Y Y

'with those values in the solid phase results in a further l Fig. 2 is an idealized curve of the temperature gradient in ingot 1 of Fig. 1 for thelposition of Vmolten zone 13 indicated. The curve of temperature against distance between cooling clamps 2 and 3 is idealized in that radiation and heat losses other than those produced axially in the direction of cooling clamps 2 and 3 are neglected. The other assumption made is that the resistivity R of ingot 1 as a function of temperature T is constant. The general form of the curve is the same for the actual case in which there is radiation or other lateral heat loss. The variation in resistivity with temperature in many materials such as the usual metallic material is such as to favor control of a molten zone produced in accordance with this invention. This will also be discussed.

For the idealized case discussed, the general form of the temperature gradient curve is parabolic and follows the general equation:

T= ms-sr u) which is the algebraic equation for an inverted Vparabola centered at x=s in which T :temperature in degrees Kelvin f Tm=maximum temperature obtained in degrees Kelvin Q=power per unit volume in watts per cubic centimeter k=thermal conductivity in watts per centimeter squared per degree C. per centimeter s=distance from a cool end of the ingot on the inside of a cooling clamp to the point of maximum temperature (Tm) in the direction of zone traversal in centimeters. NoteJ-Theposition of Tm generally corresponds with .the center of the zone.

x=distance along the ingotmeasured from the left-hand cool end in centimeters.

For the position of zone 13 shown it is seen that the curve of T against x rises lfrom a value of To at the cool end of ingot 1 to Tmp, the melting point of ingot 1 at position 14 and continues to rise to Tm, the maximum temperature at position 21 corresponding with the center of zone 13. From this peak value the curve then drops to the melting point at interface 15 which in thisv instance represents the leading solid interface of zone 13 in the direction of traversal and from there to the value T1 representing the vtemperature of the ingot at the cool end just inside cooling clamp 3. Since for the idealized case the only loss of heat is through ingot 1 into cooling blocks 2 and 3, the position of zone 13 and its length for a given power input are determined solely by end temperatures To and T1. Equations may now be presented for required sink temperatures To `and T1 in relation to zone position s.

Ti T.. 2k@ s) 3) in which l=length of ingot between clamps in centimeters from which the temperature drops are in the ratio than about one-fifth the length of the ingot between the clamps, so that, for the case in which s=0.2l, it is seen that the extreme ratio of temperature differentials, that is,

the ratio in the left-hand portion of Equation 4 is (0.2)/(0.8)2 or y. Y y

The slopes of the parabolic curve of Fig. 2 are determined by the ratioQ/Zkdn Equation 1. The greater this ratio the steeper the parabola vand the less sensitive is the length of the molten zone as a function yof temperature uctuations due, for example, to random uctuations in power input. In the zone-melting process it is generally desirable to operate with short molten zones of fixed length. y

In Fig. 2 the solid line parabolic curve is drawn for the case of constant thermal conductivity and constant electrical conductivity in the solid and liquid phases of the materiai being processed. However, for the usual system both thermal andclectrical -conductivities diter from the solid to the molten phase. As an example, for most metai systems both thermal and electrical conductivities are of the order of half as great for the molten phase, resulting, in such systems, in a ratio Q/2k in the molten phase which is about four `times that for the solid. The dashed line parabolic curve 14-15 shown on Fig. 2 is illustrative of such a system in which the thermal and electrical conductivities are less in the molten than in the solid phase. The advantages of such a system when undergoing processing in accordance with this invention are apparent; a decrease in electrical conductivity in the molten phase results in an increase in the product of 12R and a consequent increase in the amount of power generated in the molten zone, while the vaccompanying decrease in thermal conductivity results in somewhat lower axial heat ow'from the position of Tm to the solid part of the ingot, thereby resulting in a steeper gradient at the interface and better control of zone length. That advantage may be taken of this decrease in thermal and electrical conductivitiesY in the molten phase will be seen from the Illustrative Calculation l below.

Although it is apparent that an advantage is gained by use of a system in which electrical and/or thermal conductivity decreases in the .molten zone, so as to result in an increase in the value of Q/Zk, it is to be understood that this invention is not to be limited to the operation the processes described and claimed herein to systems of this nature. However, although from a. theoretical standpointv the processes herein operate effectively on any system no matter what the variation in Q/2k in the molten phase, since increase in thermal and/or electrical conductivity can result in the ultimate in no worse than constant temperature across the zone from the trailing interface to the leading interface, from -a practical standpoint it is found that a severe decrease inthe value of Q/Zk in the molten phase results in an unstable zone, the lengthof which can be controlled only by the use of extremely short ingot lengths and extremely low sink temperatures. Although such short ingot length and iow sink temperatures may be obtained effectively in virtually all non-insulating materials including germanium, silicon, and other semiconductive materials by use of species of the invention discussed, for example, in connection with Fig. 4, it has been found that for ecient operation in accordance with the apparatus of Fig. l, eiiective control over zonelength may be had only if increase in thermal and/or electrical conductivity in the zone is such as to produce a value of Q/2k which is no less'v than one-half that of the value of this ratio in the solid portion ofthe ingot.

Materials fulfilling this requirement include iron, molybdenum, titanium, zirconium, tungsten, rhenium, bismuth, and many others. VSer'tticonductive materials such as germanium and silicon sometimes have values in the molten phase which are lower than one- Illustrative Calculation 1 In accordance with this calculation power input and variation in heat sink temperatures required to move a molten zone through an iron ingot are determined. It is desired to move the center of such a zone from X =5 centimeters to X=20 centimeters in an ingot 25 centimeters long and l square centimeter in cross-sectional area. The extreme values of T0 and T1 are for the positions of the zone at X :5 and X :20 centimeters.

The thermal conductivity of solid iron is about 0.5 watt./centimeter2/ C./centimeter. The electrical resistivity in the solid phase, ps, is about 13X 10-4 ohm-centimeter at the melting point. The melting point of iron Tmp is 1540'L7 C. In accordance with experiments that have been made it is assumed that a desirable value for Tm is 16 C. above the melting point so that Tm is 1550 C. It is here assumed that the thermal conductivitics and electrical conductivities do not vary from solid to liquid phase so that ks-:kl and p,=pz. k is approximately equal to 0.5 so that Q/2k=Q/l yfor which a value of 4 is assumed. Since Q=I2p watts per cubic centimeter, the required current, I, is calculated as follows:

I: Q/p: 176 amperes For a moltenvzone centered at X =S=s, the required sink temperatures from Equations 2 and 3 are:

Still assuming equal thermal and electrical conductivities in the liquid and solid phases, the zone-length, 2(xs) is calculated yfrom Equation 1 as follows:

and

Zone length=2(xs)=3.1 centimeters The process has been discussed in terms of the idealized case in which thermal conductivity and electrical conductivity are constant throughout the ingot in both phases over the entire temperature range. In any practical system, both of these values vary. For design 'purposes variations both thermal and electrical conductivity in the solid phase may be ignored. The variation from the solid to the liquid phase,however, is significant and should `be taken into account. For the usual metal system both the electrical and' thermal conductiviti'es are about twice as great in the solid phase as -in the liquid. As a result the value 1 2k v in the liquid for such systems here designated Q'/2k, is about `four times that in the solid. Still assuming no heat loss other than axially in the direction of the sinks, the form of the thermal conductivity curve in the liquid zone remains parabolic. However, since the value is approximately four times as great as vthe curve peaks more sharply in the molten zone resulting y7 The relationshipbetween zone-length and temperature differential in the zone may bev seen from the following calculation:

' Illustrative Example 2 Assuming a temperature differential inthe molten zone of '10' C., the zone-length, 2(x-s), may be calculated as follows: g l

Y, @7216' 74)(497-0'62 (5) 2tx-s)`=true zonelength=2( 0.79) =1.6 centimeters From Equation 5 it is seen that if the temperature differential in the molten zone were to vary from about 20 degrees to about 5 degrees, within which any controlled process may be expected to operate with facility, the total variation in zone-length would be from 2.2 centimeters to -1..1 centimeters.

.Azone-length of 1.6 centimeters for iron is suitable Yforzone refining in a container, and for zone melting using the magnetic suspension vmethod of Pfann and K. D. Hagelbarger, Journal of Applied Physics 27, pages 12-18 (1956). Generally, forthe floating zone method a shorter zone, less' than 1 centimeter long, is desirable. This may be .obtained by reducing the temperature differential in the zone to about 3 C., which may be done, for example, by reducing the heating current.

Whereas variations in thermal and electrical conductivity in the case ofv a metallic system operate to the advantage `of the process, lateral losses of heat such as that due to radiation tend to decrease the control gained by variation of temperature at the heatsinks, Since, however, radiation losses are governed by a plurality of conditions and since loss by such mechanism may, in large part, Ybe controlled by andeven used to the' operators advantageby use, for example, of the apparatus discussed in yconnection with Figs. 3 and 4, exact mathematical expressions for the effect of such lateral losses are not presented. In general, since radiation losses are greater for greater temperature gradient, it is seen that the eiect of radiation is vto decrease somewhat the slopes of the axial gradients or toA flatten out the parabolic curve. Such deformation of the thermal gradient curve of Fig. 2 tends to increase the range of temperature variation at the heat sinks necessary to cause movement of the zone. Since the form of the temperature gradient curve remainsl approximately parabolic, however, a molten zone may `still lbe formed and caused to progress in accordance with the stated principles.

, Fig. 3 is illustrative of oneV type of apparatus in which radiation losses in the proximityof lthe zone are diminished.v In this ligure molten. zone 30 is formed in ingot 31 by vthe `Joule heat generated by a current which is passed axially through ingot 31 by means of a power source not shown. Heat sinks 32 and 33 may also act as end clamps and current electrodes as in Fig. 1. Motion of zone 30 may be produced-in the direction of heat sinks 33 by increasing the temperature of that sink While decreasing the temperature of sink 32 as has been described. Radiation shield 34 is moved progressively along'ingot 31 by means not shown so as -to continually encompass molten zone 30. Such a radiation shield may be made of quartz having a bright coating of platinum or other suitable heat resistant refiecting material on its inside surface.

In Fig. 4 control of the length of the molten zone is further aided by supplementing the movingl heat reflec-l tor with moving heat sinks.` Molten zone 40 is produced in ingot 41 by Joule heat generated by the passage of current axially through ingot `41 by reason of a powerfof quam-wahnsinn coating 'of bright pntinum and is moved along the rod at the same rate as molten zone 40 `by means not shown. Heat sinks 45 and 46 are also moved alongthel rod in the direction of zone travel and at the same rate on either side of heat reflector 44 and generally at fixed position relative thereto by means not shown. The heat sinks 45 and 46 depicted are cylindrical in shape, are constructed of a black body material such as graphite ora dull metal, may have fins on the inner surface and are water-cooled by means of coils 49 and 50. Moving heat sinks 45 and 46 are shown spaced from reflector 44 to keep the heat flux from the zone through interfaces 51 and 52 substantially axial. By reducing the spacing between moving reiiector 44 and moving heat sinks 45 and 46, the temperature gradients at interfaces 51 and 52 are increased in slope so that somewhat closer control of zone-length is afforded. However, close spacing will result in a large component of heat flux in a direction normal to the axis of ingot 41 resulting in interfaces 51 and 52 which are concave in the direction of the molten material. Since such concavity results in a diminution of a maximum volume of a zone which may be suspended in any of the crucible- .less zone-melting procedures, it is suggested that heat sinks 45 and 46 be spaced at such distance from reflector 44; that the heat'ux component in a direction normal to that of the axis of ingot 41 atV the interface be small compared to the axial component. A variation in the use of the apparatus of Fig. 4 depends primarily` upon positioning and/or temperatures of heat sinks 45 and 46for determining the size and location of molten-zone 40, thereby decreasing'eective ingot length and increasing control at the expense of somewhat complicating the apparatus. Control may be further enhanced by use of end blocks 42 and 43 as additionalsinks asdescribed above. l

.In the floating zone or magnetic suspension zone techniques :described above, and in other forms of crucibleless zone-melting,"`especially where the molten zone penetrates the entire cross-section vof the ingot, a clamping eiect may exist where there is appreciable expansion or contraction as the solid rod heats or cools, respectively, during the period before or after a molten zone is established. Expansion, in particular, tends to buckle the.

' molten zone is frozen in the nal position of traversal.

Even rwhere crystalline imperfections are not serious, excessive change in volume may result in the instability of the zone otherwise stable by virtue of its dimensions. An arrangement which automatically allows an ingot to expand and contract, but which, when no expansive or contractive forces are present, exerts no force on the ingot, is shown in Figs. Saand 5 b.

In the apparatus of Figs. 5a and 5b molten zone 60 is produced in ingot 61 and caused to progress in the manner already described by reason of a programming of temperatures at ixed position heat sinks on either side ot" and separated from molten zone 6i). The zone is produced b'y Joule heat resulting from the passage of current through ingot 61. The electrical path is completed by electrodes and a power source, neither of which is shown.

Clamps `62 and 63 diier from those shown in the preceding figures in that contactwith ingot 61 is through leaf mitted vby spring 64. In the event of expansion by that l portion of ingot 61 between clamps 62 and 63, duefor example, to formation of zone 60 at its initial position in the usual metal system, slippage of the serrated or threaded portion of ingot 61 within clamp 63 is permitted by spring 65. The result is a net movementof ingot 61 from left to right during each complete heating-cooling cycle. It is apparent that where a large number of molten zones are to be passed successively through an ingot such as 61 of Fig. 5a, a sufcient portion of the ingot should be allowed to project past the end of clamp 62 to allow for this movement.

This invention has been discussed primarily in terms of moving a zone of constant length through a metallic material such as iron in a crucibleless process such as the oating zone technique to which reference is made above. This procedure may be modified in many ways in accordance with current zone-melting procedures so as to obtain desired segregation characteristics in the end product.l For example, the temperatures of the heat sinks may be monitored in accordance with some program which will result in a predetermined variation in zone-length. Consequences which will follow are appar'- ent by reference to existing practices. Use of such programming may, for example, result in a uniform distribution of an impurity added to the zone in its initial position by a process sometimes referred to as starting charge only zone-melting, see United States Patent 2,739,688, issued March 20, 1956, or may result in a predetermined Variation in segregation due to changing volume of the traversing zone also disclosed in that patent, ory in sharpdistribution changes in the final product as are produced by rate-growing. If any of these procedures is to be carried'out by one of the crucibleless techniques, it is of course necessary to maintain the maximum length of the zone within the range required for stability. Such limits have been reported in the literature relating to the concerned processes, see for example above cited article by Pfann and Hagelbarger.

Although the Joule heat method of producing and causing a molten zone to traverse an ingot appears to be of primary importance for use where Crucible contamination is to be avoided by any of the techniques set forth above, it is likely that this method, due to its extreme simplicity, ready control over dimensions and rates attainable, and the inexpensive apparatus required may nd use in conjunction with any of the zone-melting procedures in which the ingot is processed in a boat or other type of crucible. From a mechanical standpoint the elimination of closely fitted moving heaters and of the heat exchange problems resulting from the use of heaters exterior to the crucible is of practical value.

Although the accompanying figures all depict the ingot under treatment with its major dimensions disposed horizontally, it is apparent that the position of the ingot will have no fundamental effect on the Joule heat method of producing the zone. Consequences which do follow by lvirtue of a displacement `of the major dimension from the horizontal are well known to those skilled in the art. Thus, crucibleless zone-melting such as by the floating f zone technique is frequently carried out with the major axis of the ingot substantially normal to the horizontal, this position resulting in a stable zone of maximum volume. Suspension zone-melting in which the zone is maintained in position by virtue of la reactive force resulting from the interaction of a current and magnetic field is generally carried out on a substantially horizontal ingot.

Other variations which are applied tov zone-melting may be utilized in conjunction with the Joule heat method herein without in any way affecting the principles of operation. Such variations include doping of the molten material, either at theinitial position of the molten zone or during traversal by solid-liquid or gas phase doping and the perturbation method of obtaining sharp varia- 10 tions in minor ingredient distribution described in United States Patent 2,739,088.

The description of this invention has been restricted to a form of molten Azone produced by Joule heating which is caused to move primarily or solely by virtue of `temperature gradients produced through the use of heat sinks. Other methods of causing Amovement of such a molten zone formed through Joule heating may, however, be substituted for the temperature gradient method described. For example, sulicient current may be passed through an ingot to raise the temperature of the solid material to within a very few degrees of its melting point .after which a molten zone may be produced by the use of-auxiliary heating equipment such, for example, as a gas torch. dn a system in which the resistivity increases upon meltingV as in the usual metallic system such a moltenl zone once formed will continue to exist by virtue of its increased resistance relative to the solid portion of the ingot and the accompanying increase in Joule heating resulting therefrom. Restriction of the crosssectional area of such a molten zoneadjacent an interface will result in the further increase in resistance in that portion of the zone with further accompanying increase in Joule heating. The net result of such an unequal distribution of Joule heating within the molten zone results in progression of that solid-liquid interface adjacent the restricted portion of the zone and regression of the other interface.

Such a restriction in cross-sectional area in a molten zone may be brought about by several alternate mechanisms. `An extremely simple method is to incline the ingot from the horizontal, thereby the redistribution of the molten material under the influence of gravity resulting in restriction of the uppermost portion of the molten zone `and expansion of the lowermost portion. Such an arrangement, therefore, results in movement of a molten zone through an ingot without the use of moving heating and/or cooling means and without the use of variable temperature heat sinks. Although such a method may result in some matter transport in the downward direction, this may be eliminated by operating at a critical tilt angle, see Transactions A.I.M.E., volume 197, page 1441, 1953.

Other methods of restricting the cross section of a molten zone at or adjacent a solid-liquid interface include moving magnetic poles so arranged as to depress the liquid over the desired area, and immersion of an inert, electrically insulating member in the molten zone at or near this interface so as to restrict the cross sectional -area of conducting liquid in this position. In such a process the magnetic poles or immersed member, must be moved with the zone.

The well-known oating zone technique naturally lends itself to use of such a Joule heating method. In accordance with such Ia process a zone is retained in position in a vertically disposed ingot between two solid portions of the ingot. Under the inuence of gravity, such a zone, retained in position solely by adhesive and cohesive forces, becomes enlarged in cross section near its lower interface and restricted near its upper. Passage of current through such a zone results in greater generation of heat near the top of the zone and consequent movement of the zone in the upward direction.

What is claimed is:

1. Method of zone-melting a non-insulating solid material comprising passing an electrical current through the material, the current being of such magnitudethat the Joule heat generated thereby is suicient to raise the material to its melting point, removing heat so generated fromv two fixed positions in the material by the use of heat sinks, the said heat sinks being in fixed positions relative to the said material, the temperatures of the sinks and mechanism of heat exchange such that there is between the sinks a molten region intermediate two solid regions, and causing at least one of the interfaces between the molten region and a 'solid regiotoprogress' by varying the amount of heat removed byat leastA one heatsink. 'H f 2. Method Yin accordance with claim 1 in which there is a thermally conductive path between the material and the heat sinks and in which the primary mechanism of heat exchange is conductive. f

3. Method in accordance with claim 2 in which there is a simultaneous variation in the amount of heat re# moved by a heat sink at each of the two positions, the

amount of heat removed being increased at one position and being decreased 'at the other position.

4. The method of claim 1 in which radiation losses in the vicinity of the molten region are reduced by use of a heat recctor.

5. The method of claim 4 in which additional cooling is produced in the solid regions adjacent the molten region by use of radiant heat absorbers.

6. The method of claim 4 in which the said material is a fusible semiconductive material.

7. The method of claim 3 in which the only solid material contacted by the said molten region is that of the said solid regions.

8. The method of claim 7 in which the value Q/Zk of the said material in the molten phase is at least as great as one-half of the value of Q/ Zik of the said material in the solid phase, in which Q equals power per unit volume of material in watts per cubic centimeter and k equals thermal conductivity in watts persquare centimeter per degrec C. per centimeter.

9. The method of claim 7 in which thedirection of progressionof the said at least one interface is substantially vertical and in which the said molten region is Vretained vab in position primarily by reason of adhesive forcesV between the said molten region and the said solid regions land cohesive forces within the said molten region.

" The method of claim 7V nawhich the. direction of progression Vof the said at least one interface is sub-v is iron.

References Cited in the le of this patent UNITED STATES PATENTS 2,149,076 Stockbarger Feb. 28, 1939 2,447,829 y Whaley Aug. 24, 1948 2,602,211 Scaff `Tuly 8,71952 2,739,088 Pfann "Marg-ZO, 1956 2,743,199 Hull et al Apr. 24, 1956 2,789,039 Jensen Apr. 16, 1957 2,801,192 Overby vJuly 30, 1957 2,875,108 Y Pfann Feb. 24, 1959 y FOREIGN PATENTS 555,214 Great Britain Aug. 10, 1943 166,223 Australia Dec. 5, 1955 OTHER REFERENCES Floating Zone Recrystallization of Silicon, Keck et y al., Review of Scientific Instruments, vol. 25, April 1954, pages 331-334. 

1. METHOD OF ZONE-MELTING A NON-INSULATING SOLID MATERIAL COMPRISING PASSING AN ELECTRICAL CURRENT THROUGH THE MATERIAL, THE CURRENT BEING OF SUCH MAGNITUDE THAT THE JOULE HEAT GENERATED THEREBY IS SUFFICIENT TO RAISE THE MATERIAL TO ITS MELTING POINT, REMOVING HEAT SO GENERATED FROM TWO FIXED POSITIONS IN THE MATERIAL BY THE USE OF HEAT SINKS, THE SAID HEAT SINKS BEING IN FIXED POSITIONS RELATIVE TO THE SAID MATERIAL, THE TEMPERATURES OF THE SINKS AND MECHANISM OF HEAT EXCHANGE SUCH THAT THERE IS BETWEEN THE SINKS A MOLTEN REGION INTERMEDIATE TWO SOLID REGIONS, AND CAUSING AT LEAST ONE OF THE INTERFACES BETWEEN THE MOLTEN REGION AND A SOLID REGION TO PROGRESS BY VARYING THE AMOUNT OF HEAT REMOVED BY AT LEAST ONE HEAT SINK. 